The Analysis Of The Connectivity For Wireless Ad Hoc Network

Wireless Ad Hoc network is a novel network. Compared to cellular network, the nodes areflexibly organized and the network doesn’t need centralized control. More attentions have been paidto Ad Hoc network. All the nodes in this network have the same characteristic. The topology canchange flexibly according to different intentions. So connectivity is especially necessary and it is animportant guarantee for the design of higher layer. This paper investigates the connectivity in AdHoc network based on stochastic geometry and graph theory.The node distribution model of Ad Hoc network is set up according to Poisson Point Process instochastic geometry. The connectivity is analysed based on disc model in one-dimension case. Inthe following, based on the depth-first search in graph theory, a node moving algorithm with signalstrength is studied, which changes the network topology from1-connectivity to2-connectivity. Aclosed formula for2-connectivity is obtained and the performance of2-connectivity is simulated.In two-dimension case, based on graph theory and considering isolated node, an SNR model inNakagami-m channel is set up. Then the probability of being no isolated node in the network isderived. The simulation identified the correctness of formula. The factors that impose theconnectivity are studied.Interference is investigated based on stochastic geometry. All the nodes are viewed as interferersbesides transmitter and receiver and the interference characteristic is obtained based on shot-noisetheory. Starting from the isolated node, the close formula for connectivity probability that there isno isolated node in the whole network is derived and is identified by simulations.Based on marked point process and CSMA, the original interferer is thinned. The newinterference distribution is obtained. In SIR model the closed formula of connectivity is derived.The simulations show that the theory value agrees well with the real value. Viewed from theconclusion, many factors such as node density, SIR threshold and carrier sense radius affect theconnectivity.